A Merging Method for Sound Pressure and Particle Velocity Signals of a Vector Hydrophone under Correlated Noise

Abstract

The present invention discloses a method for merging vector hydrophone sound pressure and velocity signals under correlated noise. Step 1: intercept the noise part of the sound pressure and velocity channel signal of the orthogonal multi-carrier bandpass continuous signal received by the vector hydrophone, and estimate the noise correlation coefficient ρ between the three channels. <subgt;ij< / subgt;,i.j∈[1,2,3];步骤2、假设多普勒因子已经被估计和补偿,多普勒扩展因子α=0,根据信道时域响应模型得到信道频域响应模型,假设各子载波的能量相等,得到声压P,振速Vx,振速Vy接收第k个子载波的信道频域响应模型;步骤3、利用声压振速互谱法得到信号源的估计方位角;步骤4、根据估计方位角和各通道噪声相关系数,计算得到声压振速通道最优加权值,合并成单通道信号。本发明在不增加复杂度的情况下,使得矢量水听器作为水下通信接收端获得更大的信噪比和更好处理增益。

Description

Technical Field

[0001] The present invention belongs to the field of underwater acoustic signal processing, and relates to a method for combining sound pressure and particle velocity signals of a vector hydrophone under correlated noise. Background Art

[0002] Compared with traditional sound pressure hydrophones, vector hydrophones are widely used in fields such as detection, positioning, and underwater communication due to advantages such as small size and light weight. In an isotropic ocean ambient noise field, the noise in the sound pressure and particle velocity channels of a single vector hydrophone is independent. For a point source, the sound pressure signal and the particle velocity signal are completely correlated. The difference in the correlation between the signals and noise in each channel of the vector hydrophone is the basis for obtaining gain in vector signal processing. In recent years, because the weighted processing of the sound pressure and particle velocity channels of the vector hydrophone can obtain a gain in spatial directivity, the vector hydrophone has been widely used in underwater communication. However, in fact, due to the non-isotropic underwater acoustic channel, the noise reaching the receiving end of the vector hydrophone is random. Coupled with the manufacturing process errors of the vector hydrophone, the noise in each channel at the receiving end is not strictly independent, so that the ambient noise power in the sound pressure and particle velocity channels does not meet the theoretical 4.8 dB difference (for a three-dimensional vector hydrophone). For the problem that the inconsistency of the ambient noise power in the sound pressure and particle velocity channels will result in loss of some processing gain, one solution is to perform maximum ratio combining weighting on the sound pressure and particle velocity channels based on the assumption of noise independence, and the other is to estimate the noise power in the sound pressure and particle velocity channels and then perform compensation.

[0003] Chinese Patent Specification CN102025424B proposes an OFDM underwater acoustic communication method based on a vector sensor, which performs weighted combination after frequency-domain passive time reversal preprocessing on the sound pressure channel and the particle velocity channel. This weighted combination is performed based on the assumption of independent noise in each channel of the vector hydrophone, and part of the processing gain will be lost due to the neglect of noise correlation. Chinese Patent Specification CN108469599B discloses a method for direction finding of a sound vector sensor with amplitude weighting MUSIC, which jointly estimates the target angle and the ambient noise power in the sound pressure and particle velocity channels to compensate for the inconsistency of the noise power in each channel. Due to the use of iterative operations, the complexity is relatively high. Summary of the Invention

[0004] Aiming at the above-mentioned prior art, the technical problem to be solved by the present invention is to provide a method for combining sound pressure and particle velocity signals of a vector hydrophone under correlated noise, which uses the optimal weighting coefficient of maximum ratio combining to obtain a larger signal-to-noise ratio and better processing gain when the vector hydrophone is used as the receiving end in underwater communication without increasing the complexity.

[0005] To solve the above technical problem, a method for combining sound pressure and particle velocity signals of a vector hydrophone under correlated noise according to the present invention includes:

[0006] Step 1: Intercept the noise parts of the acoustic pressure and vibration velocity channel signals of the quadrature multi-carrier band-pass continuous signal received by the vector hydrophone, and estimate the noise correlation coefficient ρ between the three channels, where i, j ∈ [1, 2, 3]; ij , i.j∈[1,2,3];

[0007] Step 2: Assume that the Doppler factor has been estimated and compensated, and the Doppler spread factor α = 0. Obtain the channel frequency-domain response model according to the channel time-domain response model. Assume that the energies of each sub-carrier are equal, and obtain the channel frequency-domain response models of the acoustic pressure P, vibration velocity Vx, and vibration velocity Vy for receiving the k-th sub-carrier;

[0008] Step 3: Use the acoustic pressure-vibration velocity cross-spectrum method to obtain the estimated azimuth angle of the signal source;

[0009] Step 4: Calculate the optimal weighting values of the acoustic pressure and vibration velocity channels according to the estimated azimuth angle and the noise correlation coefficients of each channel, and combine them into a single-channel signal.

[0010] Further, the channel frequency-domain response models of the acoustic pressure P, vibration velocity Vx, and vibration velocity Vy for receiving the k-th sub-carrier in Step 2 are:

[0011]

[0012] where L represents the number of underwater acoustic signal path, τ l is the time delay of the l-th path, β l is the tap coefficient, f k represents the frequency of the k-th sub-carrier, and θ is the horizontal azimuth angle of the signal source.

[0013] Further, the specific method of using the acoustic pressure-vibration velocity cross-spectrum method to obtain the estimated azimuth angle of the signal source in Step 3 is:

[0014]

[0015] where P(w) represents the acoustic pressure in the frequency domain, V x (w) and V y (w) represent the horizontal vibration velocities in the frequency domain, denotes taking the real part,

[0016] Further, the specific method of calculating the optimal weighting values of the acoustic pressure and vibration velocity channels according to the estimated azimuth angle and the noise correlation coefficients of each channel, and combining them into a single-channel signal in Step 4 is:

[0017] The power of the noise within one symbol period T satisfies:

[0018]

[0019] The three-way noise power vector N = [n1, n2, n3] T, the weighting coefficient w = [w1, w2, w3] T , E[N·N T is the cross-correlation matrix of the three-way noise and satisfies:

[0020]

[0021] Among them, is the average power of the sound path noise,

[0022]

[0023] For the k-th subcarrier, the power of the three-way weighted signal is:

[0024]

[0025] Among them, θ is the horizontal azimuth angle of the signal source, E s is the energy of each subcarrier, τ l is the delay of the l-th path, β l is the tap coefficient, f k represents the frequency of the k-th subcarrier, and L represents the number of underwater acoustic signal path;

[0026] Then the signal-to-noise ratio of the received signal at time T is:

[0027]

[0028] There exists a weight vector w such that the signal-to-noise ratio SNR is maximized, that is:

[0029]

[0030] R and Q are Hermitan matrices, and the Q matrix is positive definite. The vector w that maximizes the ratio of the two quadratic forms corresponds to the eigenvector of the largest generalized eigenvalue λ1 and satisfies:

[0031]

[0032] λ1 is the only non-zero generalized eigenvalue of R and Q, written as

[0033] det(R - λ1Q) = 0

[0034] Solve for the eigenvalue:

[0035]

[0036] Solve for the largest eigenvalue to get:

[0037]

[0038] The eigenvector w1 corresponding to λ1 satisfies the equation:

[0039] (R - λ1Q)w1 = 0

[0040] The optimal weight vector w1 that maximizes the signal-to-noise ratio SNR output by the vector hydrophone is obtained as follows:

[0041]

[0042] Furthermore, when the correlation coefficient ρ of the three-channel noise 12 = ρ 23 = ρ 13 = 0, that is, the noises of each channel are independent, the optimal weight vector w1 is:

[0043]

[0044] Advantages of the present invention: Under the condition of the correlation of the sound pressure and vibration velocity channels of the vector hydrophone, in order to improve the diversity combining performance of the sound pressure and vibration velocity channels of the vector hydrophone in a non-isotropic noise field, the present invention proposes a weighting method for maximum ratio combining of the sound pressure and vibration velocity channels of the vector hydrophone in a correlated noise field, and derives the optimal weighting coefficient for maximum ratio combining of the sound pressure and vibration velocity signals, which can enable the vector hydrophone to obtain a larger signal-to-noise ratio and better processing gain as the receiving end during underwater communication without increasing complexity. Since in the ocean waveguide, the sound wave is a standing wave in the vertical direction, for an underwater acoustic communication system, only the sound pressure signal P and the horizontal vibration velocity signals Vx and Vy can be utilized. Therefore, this method is derived based on a three-dimensional vector hydrophone and is applicable to the signal processing of the horizontal vibration velocities Vx and Vy and the sound pressure P received by the three-dimensional vector hydrophone in an underwater acoustic communication scenario. The derivation steps of this method are also applicable to a two-dimensional vector hydrophone. Compared with the prior art, the present invention has the following characteristics:

[0045] The vector hydrophone sound pressure and vibration velocity signal combining method proposed by the present invention is based on the assumption of noise correlation, and derives a signal-to-noise ratio statistical model, which conforms to the non-randomness of the actual underwater acoustic channel noise and has more practical application value;

[0046] The optimal weighting coefficient of the sound pressure and vibration velocity channels of the vector hydrophone proposed by the present invention under correlated noise is universal, and the traditional maximum ratio combining algorithm based on the assumption of independent noise is a special case of this method when the noise correlation coefficient is equal to zero;

[0047] Without increasing the system complexity, the weighting coefficient proposed by the present invention enables the bit error rate performance of the communication system to be the lowest and the output signal-to-noise ratio to be the largest. Description of the Drawings

[0048] Figure 1 It is a schematic diagram for comparing the bit error rate performance of different coefficient weightings of the sound pressure P and vibration velocity Vc of the vector hydrophone under the assumption of independent noise;

[0049] Figure 2(a) is a comparison chart of the bit error rate performance between the method proposed in the present invention and the traditional optimal method under the condition that the correlation coefficient ρ = 0.3;

[0050] Figure 2(b) is a comparison chart of the bit error rate performance between the method proposed in the present invention and the traditional optimal method under the condition that the correlation coefficient ρ = 0.6;

[0051] Figure 3 It is a schematic diagram of the bit error rate result obtained by applying the present invention to the communication experiment of the Danjiangkou Reservoir. Specific embodiments

[0052] The present invention will be further described below in conjunction with the accompanying drawings of the specification and embodiments.

[0053] The object of the present invention is achieved as follows:

[0054] 1. When processing the sound pressure and particle velocity channel signals received by the vector hydrophone, intercept the noise part and estimate the noise correlation coefficient between each channel;

[0055] 2. Taking multi-carrier frequency shift keying (MFSK) as an example, establish a multi-carrier passband signal and a vector hydrophone channel model to obtain the received sound pressure and particle velocity signals. Assume that the Doppler has been perfectly estimated and compensated, so as to obtain the sound pressure and particle velocity signals in the frequency domain;

[0056] 3. Use the sound pressure and particle velocity cross-spectrum method to obtain the estimated azimuth angle of the signal source;

[0057] 4. With the help of parameters such as the estimated azimuth angle and the noise correlation coefficient of each channel, calculate the optimal weighting value of the sound pressure and particle velocity channels, and merge them into a single-channel signal as the input signal of the decoder. The present invention includes the following steps:

[0058] A. Estimate the noise correlation coefficient

[0059] For the received sound pressure and particle velocity channels, intercept the noise part and estimate the noise correlation coefficient ρ of the three channels ij , i.j ∈ [1, 2, 3];

[0060] B. Preprocess the sound pressure and particle velocity signals

[0061] Taking multi-carrier MFSK as an example, the time-domain waveform expression of the transmitted band-pass continuous signal

[0062]

[0063] where represents the frequency of the k-th sub-carrier, K represents the total number of sub-carriers, s[k] represents the symbol of the k-th sub-carrier of MFSK, and t represents the signal duration. If there are L paths in the underwater acoustic channel and the delay of the l-th path is τl , the tap coefficient β l , the channel is expressed as Assume that the Doppler factor has been perfectly estimated and compensated. It is reasonable to assume that the Doppler spread factor α = 0, and the corresponding channel frequency response is Let the energy of each sub - carrier in the MFSK system be Es. Then the sound pressure P, the vibration velocity Vx, and the vibration velocity Vy of the received k - th sub - carrier's channel frequency response are

[0064]

[0065] where θ is the horizontal azimuth angle of the signal source. In the above formula, the background noise of the three channels is set as independent Gaussian white noise, and the average power of the sound pressure channel noise is It is pointed out that in an isotropic noise field, the autocorrelation coefficient of the sound pressure channel is 1, and the autocorrelation coefficients of the vibration velocities in the Vx and Vy directions are 1 / 3. From the characteristics of Gaussian white noise with a mean of 0, the average power of the vibration velocity channel is

[0066] When the horizontal azimuth angle of the signal source is equal to the guiding azimuth angle, the signal - to - noise ratios of the sound pressure P(w) and the horizontal vibration velocities V x (w), V y (w) of the three - path signals are

[0067]

[0068] C. Azimuth angle estimation

[0069] In the ocean channel, Ohm's law is approximately satisfied, and the sound pressure and vibration velocity are in the same phase. The azimuth angle can be estimated using the frequency - domain sound pressure P(w) and the horizontal vibration velocities V x (w), V y (w):

[0070]

[0071] denotes taking the real part. Since this method focuses on the weighting technology of the sound pressure and vibration velocity signals, the classical cross - spectral method is used to roughly estimate the azimuth angle.

[0072] D. Weighting of sound pressure and vibration velocity signals based on correlated noise

[0073] In a symbol period T, it can be considered that the additive noise is wide - sense stationary. So the power of the noise within time T

[0074]

[0075] Here, the three - path noise power vector N = [n1, n2, n3] T , and the weighting coefficient w = [w1, w2, w3]T , E[N·N T is the cross-correlation matrix of the three-way noise, and there is

[0076]

[0077] For the k-th subcarrier, the signal power after three-way weighting is

[0078]

[0079] where

[0080] Therefore, the signal-to-noise ratio of the received signal at time T is obtained as

[0081]

[0082] That is, there exists a weight vector w such that the signal-to-noise ratio SNR is maximized, i.e.,

[0083]

[0084] R and Q are Hermitan matrices, and the Q matrix is positive definite. Then the vector w that maximizes the ratio of the two quadratic forms corresponds to the eigenvector of the largest generalized eigenvalue λ1, and there is

[0085]

[0086] Because rank(R) = 1, so λ1 is the only non-zero generalized eigenvalue of R and Q, written as

[0087] det(R - λ1Q) = 0 (11)

[0088] Solving for the eigenvalue, there is

[0089]

[0090] Solving for the largest eigenvalue gives

[0091]

[0092] The eigenvector w1 corresponding to λ1 satisfies the equation

[0093] (R - λ1Q)w1 = 0 (14)

[0094] The solution is

[0095]

[0096] Therefore, the combination method of the optimal weight vector w1 in the above formula maximizes the signal-to-noise ratio SNR of the output of the vector hydrophone,

[0097]

[0098] In particular, when the correlation coefficient of the three-channel noise is 12 =ρ 23 =ρ 13 = 0, that is, the noise of each channel is independent, then q 12 =q 23 =q 13 =0, corresponding weight

[0099]

[0100] Signal-to-noise ratio (SNR)

[0101]

[0102] Therefore, the traditional maximum ratio combining method based on noise independence is a special case of the present invention. The present invention can obtain the optimal weighting coefficient by solving the noise correlation coefficient and estimating the azimuth angle, so as to maximize the processing gain of the receiving end.

[0103] Figure 1 Figure 3 is a schematic diagram comparing the bit error rate performance of vector hydrophones with different weighting coefficients for sound pressure P and vibration velocity Vc under the assumption of independent noise. In this case, the method proposed in the present invention and the traditional maximum ratio combining algorithm have the same weighting coefficients when processing sound pressure and vibration velocity, and exhibit the best bit error performance.

[0104] Figure 2(a) and 2(b) This is a comparison chart of the bit error rate performance of the method proposed in the present invention and the traditional optimal method under the conditions of correlation coefficient ρ = 0.3 and ρ = 0.6. When the correlation coefficient ρ = 0.3, the algorithm proposed in the present invention has a gain of about 1.5dB compared with the traditional maximum ratio combining algorithm based on noise independence, and when the correlation coefficient ρ = 0.6, it has a gain of about 2.5dB.

[0105] Figure 3 This diagram shows the bit error rate results obtained from a communication experiment using the present invention at the Danjiangkou Reservoir. The experimental data demonstrates that in a realistic underwater channel environment, there is a certain correlation between the vector hydrophone's sound pressure velocity channel noise, and that the proposed method significantly improves the system's bit error rate performance. Under these channel conditions, the proposed method demonstrates a gain of approximately 2.5dB compared to traditional processing methods.

[0106] The above steps are only for explaining the technical concept of the present invention and are not intended to limit the present invention. Any changes, improvements, etc. made to the technical solutions, technical concepts, and introduction methods proposed in the present invention shall fall within the scope of protection of the present invention.

Claims

1. A method for combining sound pressure and particle velocity signals of a vector hydrophone under correlated noise, characterized in that, include: Step 1: intercept the noise part of the sound pressure velocity channel signal of the orthogonal multi-carrier bandpass continuous signal received by the vector hydrophone, and estimate the noise correlation coefficient ρ between the three channels ij ,ij∈[1,2,3]; Step 2: Assuming that the Doppler factor has been estimated and compensated, and the Doppler expansion factor α = 0, obtain the channel frequency domain response model based on the channel time domain response model. Assuming that the energy of each subcarrier is equal, obtain the sound pressure P, vibration velocity Vx, and vibration velocity Vy of the channel frequency domain response model for receiving the kth subcarrier; Step 3: Use the sound pressure-velocity cross-spectrum method to obtain the estimated azimuth of the signal source; Step 4: Calculate the optimal weighted value of the sound pressure and velocity channels based on the estimated azimuth angle and the noise correlation coefficient of each channel, and merge them into a single channel signal; The noise power in a symbol period T satisfies: Three-way noise power vector N = [n1, n2, n3] T , weighting coefficient w=[w1,w2,w3] T , E[N·N T ] is the cross-correlation matrix of the three-way noise, satisfying: Among them, is the average power of the sound pressure road noise, For the kth subcarrier, the three-way weighted signal power is: Among them, θ is the horizontal azimuth angle of the signal source, E s is the energy of each subcarrier, τ l is the time delay of the l-th path, β l is the tap coefficient, f k represents the frequency of the k-th subcarrier, and L represents the number of underwater acoustic channel paths; Then the signal-to-noise ratio of the received signal at time T is:

2. A method for combining sound pressure and particle velocity signals of a vector hydrophone under correlated noise according to claim 1, characterized in that: The channel frequency domain response model of the sound pressure P, vibration velocity Vx, and vibration velocity Vy for receiving the kth subcarrier in step 2 is: Among them, \(L\) represents the number of underwater acoustic channel paths, and \(\tau\) l is the time delay of the \(l\)-th path, and \(\beta\) l is the tap coefficient, \(f\) k represents the frequency of the \(k\)-th subcarrier, and \(\theta\) is the horizontal azimuth angle of the signal source.

3. The method for merging vector hydrophone sound pressure and velocity signals under correlated noise according to claim 1, characterized in that: The method of using the sound pressure-velocity cross-spectrum method to obtain the estimated azimuth angle of the signal source in step 3 is specifically as follows: Where P(w) represents the frequency domain sound pressure, V x (w) and V y (w) represents the horizontal vibration velocity in the frequency domain, Indicates taking the real part.

4. A method for combining sound pressure and particle velocity signals of a vector hydrophone under correlated noise according to claim 1, characterized in that: In step 4, there is a weight vector w that maximizes the signal-to-noise ratio SNR, namely: R and Q are Hermitian matrices, and the Q matrix is positive definite. The vector w that maximizes the ratio of the two quadratic forms corresponds to the eigenvector of the largest generalized eigenvalue λ1, satisfying: λ1 is the only non-zero generalized eigenvalue of R and Q, written as det(R-λ1Q)=0 Solve for the eigenvalues: Find the maximum eigenvalue: The eigenvector w1 corresponding to λ1 satisfies the equation: (R-λ1Q)w1=0 The optimal weight vector w1 that maximizes the signal-to-noise ratio (SNR) output by the vector hydrophone is obtained as follows:

5. The method for merging vector hydrophone sound pressure and velocity signals under correlated noise according to claim 4, characterized in that: When the correlation coefficient of the three-channel noise ρ 12 =ρ 23 =ρ 13 = 0, that is, the noise of each channel is independent, and the optimal weight vector w1 is:

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